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Null hypothesis *H_0: m0 = m0’* is tested versus
alternative hypothesis *H_1: m0 neq m0’*.
Test criterion is ratio of a posteriori estimate of
reference standard deviation

m0' = sqrt( v'P v / |

and a priori reference standard deviation m0 (input data parameter
`m0-apr`

). For given significance level *alpha* lower and
upper bounds of interval *(L, U)* are computed so, that if
hypothesis *H_0* is true, probabilities *P(m0’/m0
le D)* and *P(m0’/m0 ge H)* are equal to
*alpha/2*. Lower and upper bounds of the interval are computed as

L = sqrt((Chi^2_{1-alpha/2, |

Probability

` P(L < m0'/m0 < U) = ` |

is by default 95%, this corresponds to 5% confidence level test.

Exceeding the upper limit *H* of the confidence interval can be
caused even by a single gross error (one outlying observation).
Method of Least Squares is generally very sensitive to presence of
outliers. Safely can be detected only one observation whose elimination
leads to maximal decrease of a posteriori estimate of reference standard
deviation

(6) m0'' = sqrt{(v'P v - delta)/( |

where

(7) q_vi = 1/p_i - q_Li |

is weight coefficient of *i*-th residual. If the set of
observations contains only one gross error, the outlying observation is
likely to be detected, but this can not be guaranteed.

In addition, program `gama-local`

computes a posteriori estimate
of reference standard deviation separately for horizontal distances
and directions and/or angles after formula from

m0'_t = sqrt(sum{~v^2_it}) / sum{~q_vi}), t=d,s, |

where symbol *t* denotes observed distances, directions and/or
angles.

m0 apriori : 10.00 m0' empirical: 9.64 [pvv] : 3.43560e+03 During statistical analysis we work - with empirical standard deviation 9.64 - with confidence level 95 % Ratio m0' empirical / m0 apriori: 0.964 95 % interval (0.773, 1.227) contains value m0'/m0 m0'/m0 (distances): 0.997 m0'/m0 (directions): 0.943 Maximal decrease of m0''/m0 on elimination of one observation: 0.892 Maximal studentized residual 2.48 exceeds critical value 1.95 on significance level 5 % for observation #35 <distance from="407" to="422" val="346.415" stdev="5.0" /> |

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